Skip to main content
Log in

A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

An overview of present understanding of microstructure in flowing suspensions is provided. An emphasis is placed on how the microstructure leads to observable bulk flow phenomena unique to mixtures. The bridge between the particle and bulk scales is provided by the mixture rheology; one focus of the review is on work that addresses the connection between microstructure and rheology. The non-Newtonian rheology of suspensions includes the well-known rate dependences of shear thinning and thickening, which have influence on bulk processing of suspensions. Shear-induced normal stresses are also measured in concentrated suspensions and include normal stress differences, and the isotropic particle pressure. Normal stresses have been associated with shear-induced migration, and thus have influence on the ultimate spatial distribution of solids, as well as the flow rate during processing; a second focus is on these uniquely two-phase behaviors and how they can be described in terms of the bulk rheology. An important bulk fluid mechanical consequence of normal stresses is their role in driving secondary flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Abbott JR, Tetlow N, Graham AL, Altobelli SA, Fukushima E, Mondy LA, Stephens TS (1991) Experimental observations of particle migration in concentrated suspensions: Couette flow. J Rheol 35:773

    Article  ADS  CAS  Google Scholar 

  • Ackerson BJ (1990) Shear induced order and shear processing of model hard-sphere suspensions. J Rheol 34:553

    Article  ADS  Google Scholar 

  • Aidun CK, Lu Y, Ding EJ (1998) Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J Fluid Mech 373:287

    Article  ADS  CAS  Google Scholar 

  • Altobelli SA, Givler RC, Fukushima E (1991) Velocity and concentration measurements of suspensions by nuclear magnetic resonance imaging. J Rheol 35:721

    Article  ADS  CAS  Google Scholar 

  • Ball RC, Melrose JR (1995) Lubrication breakdown in hydrodynamic simulations of concentrated colloids. Adv Colloid Interface Sci 59:19

    Article  CAS  Google Scholar 

  • Barnes HA (1989) Shear-thickening (dilatancy) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids. J Rheol 33:329

    Article  ADS  CAS  Google Scholar 

  • Banchio AJ, Brady JF (2003) Accelerated Stokesian Dynamics: brownian motion. J Chem Phys 118:10323

    Article  ADS  CAS  Google Scholar 

  • Batchelor GK (1970) The stress system in a suspension of force-free particles. J Fluid Mech 41:545

    Article  ADS  MathSciNet  Google Scholar 

  • Batchelor GK (1977) The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech 83:97

    Article  ADS  MathSciNet  Google Scholar 

  • Batchelor GK, Green JT (1972a) The hydrodynamic interation of two small freely-moving spheres in a linear flow field. J Fluid Mech 56:375

    Article  ADS  Google Scholar 

  • Batchelor GK, Green JT (1972b) Determination of bulk stress in a suspension of spherical-particles to order c 2. J Fluid Mech 56:401

    Article  ADS  Google Scholar 

  • Bender JW, Wagner NJ (1995) Optical measurement of the contributions of colloidal forces to the rheology of concentrated colloidal dispersions. J Colloid Interface Sci 172:171

    Article  CAS  Google Scholar 

  • Bender JW, Wagner NJ (1996) Reversible shear thickening in monodisperse and bidisperse colloidal dispersions. J Rheol 40:899

    Article  ADS  CAS  Google Scholar 

  • Bergenholtz J (2001) Theory of rheology of colloidal dispersions. Curr Opin Colloid Interface Sci 6:484

    Article  CAS  Google Scholar 

  • Bergenholtz J, Brady JF, Vicic MA (2002) The non-Newtonian rheology of dilute colloidal suspensions. J Fluid Mech 456:239

    Article  ADS  CAS  Google Scholar 

  • Bossis G, Meunier A, Brady JF (1991) Hydroynamic stress on fractal aggregates of spheres. J Chem Phys 94:5064

    Article  ADS  Google Scholar 

  • Brader JM, Cates ME, Fuchs M (2008) First-principles constitutive equation for suspension rheology. Phys Rev Lett 101:138301

    Article  PubMed  ADS  CAS  Google Scholar 

  • Brady JF, Morris JF (1997) Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J Fluid Mech 348:103

    Article  ADS  CAS  Google Scholar 

  • Brady JF, Vicic MA (1995) Normal stresses in colloidal dispersions. J Rheol 39:545

    Article  ADS  CAS  Google Scholar 

  • Brady JF, Bossis G (1988) Stokesian Dynamics. Ann Rev Fluid Mech 20:111

    Article  ADS  Google Scholar 

  • Butler JE, Majors PD, Bonnecaze RT (1999) Observations of shear-induced particle migration for oscillatory flow of a suspension within a tube. Phys Fluids 11:2865

    Article  ADS  CAS  Google Scholar 

  • Chang CY, Powell RL (1993) Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particles. J Fluid Mech 253:1

    Article  ADS  CAS  Google Scholar 

  • Chow AW, Iwayima JH, Sinton SW, Leighton DT (1995) Particle migration of non-Brownian, concentrated suspensions in a truncated cone-and-plate. Soc. Rheology Mtg, Sacramento

    Google Scholar 

  • Davis RH, Zhao Y, Galvin KP, et al (2003) Solid-solid contacts due to surface roughness and their effects on suspension behaviour. Phil Trans R Soc Lond A 361:871

    Article  ADS  MathSciNet  Google Scholar 

  • Deboeuf A, Gauthier G, Martin J, Yurkovetsky Y, Morris JF (2009) Particle pressure in a sheared suspension: a bridge from osmosis to granular dilatancy. Phys Rev Lett 102:108301

    Google Scholar 

  • D’Haene P, Mewis J, Fuller GG (1993) Scattering dichroism measurements of flow-induced structure of a shear thickening suspension. J Colloid Interface Sci 156:350

    Article  Google Scholar 

  • Dhont JKG, Briels WJ (2008) Vorticity and gradient banding. Rheol Acta 47:257

    Article  CAS  Google Scholar 

  • Doi M, Edwards SF (1988) The theory of polymer dynamics. Oxford Science, Oxford

    Google Scholar 

  • Drew DA, Lahey RT (1993) Analytical modeling of multiphase flow. In: Roco MC (ed) Particulate two-phase flows. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Foss DR, Brady JF (2000) Structure, diffusion and rheology of Brownian suspensions by Stokesian Dynamics simulation. J Fluid Mech 407:167

    Article  ADS  CAS  Google Scholar 

  • Frank M, Anderson D, Weeks ER, Morris JF (2003) Particle migration in pressure-driven flow of a Brownian suspension J Fluid Mech 493:363

    Article  ADS  Google Scholar 

  • Fuchs M, Cates ME (2002) Theory of nonlinear rheology and yielding of dense colloidal suspensions. Phys Rev Lett 89:248304

    Article  PubMed  ADS  Google Scholar 

  • Giesekus H (1965) Sekundarstromungen in viskoelastischen Flussigkeiten bei stationarer und periodischer Bewegung. Rheol Acta 4:85

    Article  CAS  Google Scholar 

  • Goddard JD (1984) Dissipative materials as models of thixotropy and plasticity. J Non-Newton Fluid Mech 14:141

    Article  CAS  Google Scholar 

  • Goddard JD (2006) A dissipative anisotropic fluid model for non-colloidal particle dispersions. J Fluid Mech 568:1

    Article  ADS  MathSciNet  Google Scholar 

  • Hammond PS (1995) Settling and slumping in a Newtonian slurry, and implications for proppant placement during hydraulic fracturing of gas wells. Chem Eng Sci 50:3247

    Article  CAS  Google Scholar 

  • Hoffman RL (1972) Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability. Trans Soc Rheol 16:155

    Article  CAS  Google Scholar 

  • Jeffrey DJ, Morris JF, Brady JF (1993) The pressure moments for two spheres in a low-Reynolds-number flow. Phys Fluids A 5:2317

    Article  ADS  CAS  Google Scholar 

  • Jeffrey DJ, Onishi Y (1984) Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J Fluid Mech 139:261

    Article  ADS  Google Scholar 

  • Jenkins JT, McTigue DF (1990) Transport process in concentrated suspensions: the role of particles fluctuations. In: Joseph DD, Schaeffer DG (eds) Two phase flows and waves. Springer, New York

    Google Scholar 

  • Jomha A, Reynolds P (1993) An experimental study of the first normal stress difference-shear stress relationship in simple shear flow for concentrated shear thickening suspensions. Rheol Acta 32:457

    Article  CAS  Google Scholar 

  • Keller DS, Keller DV (1991) The effect of particle-size distribution on the antithixotropic and shear thickening properties of coal-water dispersions. J Rheol 35:1583

    Article  ADS  CAS  Google Scholar 

  • Koh CJ, Hookham P, Leal LG (1994) An experimental investigation of concentrated suspension flows in a rectangular channel. J Fluid Mech 266:1

    Article  ADS  CAS  Google Scholar 

  • Kolli VG, Pollauf EJ, Gadala-Maria F (2002) Transient normal stress response in a concentrated suspension of spherical particles. J Rheol 46:321

    Article  ADS  CAS  Google Scholar 

  • Krieger IM (1972) Rheology of monodisperse latices. Adv Colloid Interface Sci 3:111

    Article  CAS  Google Scholar 

  • Kulkarni SD, Morris JF (2009) Ordering transition and structural evolution under shear in Brownian suspensions. J Rheol 53:417

    Article  ADS  CAS  Google Scholar 

  • Ladd AJC, Verberg R (2001) Lattice-Boltzmann simulations of particle-fluid suspensions. J Stat Phys 104:1191

    Article  CAS  MathSciNet  Google Scholar 

  • Laun H (1994) Normal stresses in extremely shear thickening polymer dispersions. J Non-Newton Fluid Mech 54:87

    Article  CAS  Google Scholar 

  • Leighton DT, Acrivos A (1986) Viscous resuspension. Chem Eng Sci 41:1377

    Article  CAS  Google Scholar 

  • Leighton DT, Acrivos A (1987) The shear-induced migration of particles in concentrated suspensions. J Fluid Mech 181:415

    Article  ADS  CAS  Google Scholar 

  • Lionberger RA (1998) Shear thinning of colloidal dispersions. J Rheol 42:843

    Article  ADS  CAS  Google Scholar 

  • Lionberger RA, Russel WB (1997a) Effectiveness of nonequilibrium closures for the many body forces in concentrated colloidal dispersions. J Chem Phys 106(1):402

    Article  ADS  CAS  Google Scholar 

  • Lionberger RA, Russel WB (1997b) A Smoluchowski theory with simple approximations for hydrodynamic interactions in concentrated dispersions. J Rheol 41:399

    Article  ADS  CAS  Google Scholar 

  • Lootens D, Hébraud P, Lécolier E, van Damme H (2004) Gelation, shear-thinning and shear-thickening in cement slurries. Oil Gas Sci Technol 59:31

    Article  CAS  Google Scholar 

  • Lootens D, van Damme H, Hémar, Y, Hébraud P (2005) Dilatant flow of concentrated suspensions of rough particles. Phys Rev Lett 95:268302

    Article  PubMed  ADS  Google Scholar 

  • Lyon MK, Leal LG (1998a) An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. J Fluid Mech 363:25

    Article  ADS  CAS  Google Scholar 

  • Lyon MK, Leal LG (1998b) An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 2. Bidisperse systems. J Fluid Mech 363:57

    Article  ADS  CAS  Google Scholar 

  • MacMeccan RM, Clausen JR, Neitzel GP, Aidun CK (2009) Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method. J Fluid Mech 618:13

    Article  ADS  MathSciNet  Google Scholar 

  • Maranzano BJ, Wagner NJ (2002) Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transition. J Chem Phys 117:10291

    Article  ADS  CAS  Google Scholar 

  • Martys NS (2005) Study of a dissipative particle dynamics based approach for modeling suspensions. J Rheol 49:401

    Article  ADS  CAS  Google Scholar 

  • Melrose JR, Ball RC (2004a) Continuous shear thickening transitions in model concentrated colloids—The role of interparticle forces. J Rheol 48:937

    Article  ADS  CAS  Google Scholar 

  • Melrose JR, Ball RC (2004b) “Contact networks” in continuously shear thickening colloids. J Rheol 48:961

    Article  ADS  CAS  Google Scholar 

  • Miller RM, Morris JF (2006) Normal stress-driven migration and axial development in pressure-driven flow of a concentrated suspension. J Non-Newton Fluid Mech 135:149

    Article  CAS  Google Scholar 

  • Moraczewski T, Tang HY, Shapley NC (2005) Flow of a concentrated suspension through an abrupt axisymmetric expansion measured by nuclear magnetic resonance imaging. J Rheol 49:1409

    Article  ADS  CAS  Google Scholar 

  • Morris JF, Boulay F (1999) Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J Rheol 43:1213

    Article  ADS  CAS  Google Scholar 

  • Morris JF, Brady JF (1998) Pressure-driven flow of a suspension: buoyancy effects. Int J Multiphase Flow 24:105

    Article  CAS  Google Scholar 

  • Morris JF, Katyal B (2002) Microstructure from simulated Brownian suspension flow at large shear rate. Phys Fluids 14:1920

    Article  ADS  CAS  Google Scholar 

  • Newstein MC, Wang H, Balsara NP, et al (1999) Microstructural changes in a colloidal liquid in the shear thinning and shear thickening regimes. J Chem Phys 111:4827

    Article  ADS  CAS  Google Scholar 

  • Nguyen QD, Boger DV (1998) Application of rheology to solving tailings disposal problems. Int J Mineral Process 54:217

    Article  CAS  Google Scholar 

  • Norman JT, Oguntade BO, Bonnecaze RT (2008) Particle-phase distributions of pressure-driven flows of bidisperse suspensions. J Fluid Mech 594:1

    Article  ADS  CAS  Google Scholar 

  • Nott PR, Brady JF (1994) Pressure-driven flow of suspensions: simulation and theory. J Fluid Mech 275:157

    Article  ADS  CAS  Google Scholar 

  • Ovarlez G, Bertrand F, Rodts S (2006) Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. J Rheol 50:259

    Article  ADS  CAS  Google Scholar 

  • Parsi F, Gadala-Maria F (1987) Fore-and-aft asymmetry in a concentrated suspension of solid spheres. J Rheol 31:725

    Article  ADS  CAS  Google Scholar 

  • Phung TN, Brady JF, Bossis G (1996) Stokesian Dynamics simulation of brownian suspensions. J Fluid Mech 313:181

    Article  ADS  CAS  Google Scholar 

  • Pine DJ, Gollub JP, Brady JF, Leshansky AM (2005) Chaos and threshold for irreversibility in sheared suspensions. Nature 438:997

    Article  PubMed  ADS  CAS  Google Scholar 

  • Prasad D, Kytömaa HK (1995) Particle stress and viscous compaction during shear of dense suspensions. Int J Multiph Flow 21:775

    Article  CAS  Google Scholar 

  • Rampall I, Smart J, Leighton DT (1997) The influence of surface roughness on the pair particle distribution function of dilute suspensions of non-colloidal spheres in simple shear flow. J Fluid Mech 339:1

    Article  ADS  CAS  Google Scholar 

  • Ramachandran A, Leighton DT (2007) Viscous resuspension in a tube: the impact of secondary flows resulting from second normal stress differences. Phys Fluids 19:053301

    Article  ADS  Google Scholar 

  • Ramachandran A, Leighton DT (2008) The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions. J Fluid Mech 603:207

    Article  ADS  MathSciNet  Google Scholar 

  • Russel WB, Saville DA, Schowalter WR (1989) Colloidal dispersions. Cambridge University Press, Cambridge

    Google Scholar 

  • Semwogerere D, Morris JF, Weeks ER (2007) Development of particle migration in pressuredriven flow of a Brownian suspension. J Fluid Mech 581:437

    Article  ADS  Google Scholar 

  • Sierou A, Brady JF (2001) Accelerated Stokesian Dynamics simulations. J Fluid Mech 448:115

    Article  ADS  CAS  Google Scholar 

  • Sierou A, Brady JF (2002) Rheology and microstructure in concentrated noncolloidal suspensions. J Rheol 46:1031

    Article  ADS  CAS  Google Scholar 

  • Singh A, Nott PR (2000) Normal stresses and microstructure in bounded sheared suspensions via Stokesian Dynamics simulations. J Fluid Mech 412:279

    Article  ADS  CAS  Google Scholar 

  • Singh A, Nott PR (2003) Experimental measurements of the normal stresses in sheared Stokesian suspensions. J Fluid Mech 490:293

    Article  ADS  CAS  Google Scholar 

  • Stickel JJ, Phillips RJ, Powell RL (2006) A constitutive model for microstructure and total stress in particulate suspensions. J Rheol 50:379

    Article  ADS  CAS  Google Scholar 

  • Stickel JJ, Phillips RJ, Powell RL (2007) Application of a constitutive model for particulate suspensions: time-dependent viscometric flows. J Rheol 51:1271

    Article  ADS  CAS  Google Scholar 

  • Stickel JJ, Powell RL (2005) Fluid mechanics and rheology of dense suspensions. Ann Rev Fluid Mech 37:129

    Article  ADS  MathSciNet  Google Scholar 

  • Subia SR, Ingber MS, Mondy LA, Altobelli SA, Graham AL (1998) Modelling of concentrated suspensions using a continuum constitutive equation. J Fluid Mech 373:193

    Article  ADS  Google Scholar 

  • van der Werff JC, de Kruif CG (1989) Hard-sphere colloidal dispersions: the scaling of rheological properties with particle size, volume fraction, and shear rate. J Rheol 33:421

    Article  Google Scholar 

  • Vieira SL, Neto LBP, Arruda ACF (2000) Transient behavior of an electrorheological fluid in shear flow mode. J Rheol 44:1139

    Article  ADS  CAS  Google Scholar 

  • von Pfeil K, Graham MD, Klingenberg DJ, Morris JF (2002) Pattern formation in flowing electrorheological fluids. Phys Rev Lett 88:188301

    Article  ADS  Google Scholar 

  • Wilson HJ (2005) An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. J Fluid Mech 534:97

    Article  ADS  MathSciNet  Google Scholar 

  • Xi CG, Shapley NC (2008) Flows of concentrated suspensions through an asymmetric bifurcation. J Rheol 52:625

    Article  ADS  CAS  Google Scholar 

  • Yurkovetsky Y, Morris JF (2006) Triplet correlation in sheared suspensions of Brownian particles. J Chem Phys 124:204908

    Article  PubMed  ADS  Google Scholar 

  • Yurkovetsky Y, Morris JF (2008) Particle pressure in a sheared Brownian suspension. J Rheol 52:141

    Article  ADS  CAS  Google Scholar 

  • Yziquel F, Carreau PJ, Moan M, Tanguy PA (1999) Rheological modeling of concentrated colloidal suspensions. J Non-Newton Fluid Mech 86:133

    Article  CAS  Google Scholar 

  • Zarraga IE, Hill DA, Leighton DT (2000) The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J Rheol 44:185

    Article  ADS  CAS  Google Scholar 

  • Zarraga IE, Hill DA, Leighton DT (2001) Normal stresses and free surface deformation in concentrated suspensions of noncolloidal spheres in a viscoelastic fluid. J Rheol 45:1065

    Article  ADS  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeffrey F. Morris.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morris, J.F. A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol Acta 48, 909–923 (2009). https://doi.org/10.1007/s00397-009-0352-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-009-0352-1

Keywords

Navigation